General decay of a nonlinear viscoelastic wave equation with
Balakrishn\^{a}n-Taylor damping and a delay
involving variable source
Abstract
This paper is devoted to the stability of a viscoelastic problem with
Balakrishn\^{a}n-Taylor damping and time delay
involving variable-exponent nonlinearity. Under some assumptions on the
relaxation function, we establish the general decay estimate for the
energy via suitable Lyapunov functionals. The problem considered is
novel and meaningful because the presence of the flutter panel equation
and the spillover problem with memory and variable exponents time delay
control. Our result generalizes and improves previous conclusion in the
literature.